Posthemorrhagic hydrocephalus is a frequent and difficult management problem following intraventricular hemorrhage (IVH) in the preterm infant. This protocol is designed to test the hypothesis that hydrocephalus in most infants spontaneously regresses and that outcome in those infants is no different than in infants whose hydrocephalus is managed by therapeutic intervention. All infants with IVH will be followed with cranial ultrasound for development of progressive ventricular dilatation, i.e., hydrocephalus. Infants with severe hydrocephalus will be randomized into either a No Treatment or a Lumbar Puncture Group. The infants then will be followed closely by serial ultrasound and clinical examination for progression of hydrocephalus. Study failure occurs if progression continues. Outcome of the infants will be assessed at yearly intervals, with a final assessment of outcome on each infant at three years of age.